2,455 research outputs found
Dissipative flow and vortex shedding in the Painlev\'e boundary layer of a Bose Einstein condensate
Raman et al. have found experimental evidence for a critical velocity under
which there is no dissipation when a detuned laser beam is moved in a
Bose-Einstein condensate. We analyze the origin of this critical velocity in
the low density region close to the boundary layer of the cloud. In the frame
of the laser beam, we do a blow up on this low density region which can be
described by a Painlev\'e equation and write the approximate equation satisfied
by the wave function in this region. We find that there is always a drag around
the laser beam. Though the beam passes through the surface of the cloud and the
sound velocity is small in the Painlev\'e boundary layer, the shedding of
vortices starts only when a threshold velocity is reached. This critical
velocity is lower than the critical velocity computed for the corresponding 2D
problem at the center of the cloud. At low velocity, there is a stationary
solution without vortex and the drag is small. At the onset of vortex shedding,
that is above the critical velocity, there is a drastic increase in drag.Comment: 4 pages, 4 figures (with 9 ps files
Some Remarks about Variable Mass Systems
We comment about the general argument given to obtain the rocket equation as
it is exposed in standard textbooks. In our opinion, it can induce students to
a wrong answer when solving variable mass problems.Comment: 2 page
Radiative damping: a case study
We are interested in the motion of a classical charge coupled to the Maxwell
self-field and subject to a uniform external magnetic field, B. This is a
physically relevant, but difficult dynamical problem, to which contributions
range over more than one hundred years. Specifically, we will study the
Sommerfeld-Page approximation which assumes an extended charge distribution at
small velocities. The memory equation is then linear and many details become
available. We discuss how the friction equation arises in the limit of "small"
B and contrast this result with the standard Taylor expansion resulting in a
second order equation for the velocity of the charge.Comment: 4 figure
About Superluminal motions and Special Relativity: A Discussion of some recent Experiments, and the solution of the Causal Paradoxes
Some experiments, performed at Berkeley, Cologne, Florence, Vienna, Orsay,
Rennes, etc., led to the claim that something seems to travel with a group
velocity larger than the speed c of light in vacuum. Various other experimental
results seem to point in the same direction: For instance, localized wavelet-
type solutions to Maxwell equations have been found, both theoretically and
experimentally, that travel with superluminal speed. [Even muonic and
electronic neutrinos [it has been proposed] might be "tachyons", since their
square mass appears to be negative]. With regard to the first-mentioned
experiments, it was recently claimed by Guenter Nimtz that those results with
evanescent waves (or tunneling photons) imply superluminal signal and impulse
transmission, and therefore violate Einstein causality. In this note we want to
stress that, on the contrary, all such results do not place relativistic
causality in jeopardy, even if they referred to actual tachyonic motions: In
fact, Special Relativity can cope even with superluminal objects and waves. For
instance, it is possible (at least in microphysics) to solve also the known
causal paradoxes, devised for faster than light motion, although this is not
widely recognized yet. Here we show, in detail and rigorously, how to solve the
oldest causal paradox, originally proposed by Tolman, which is the kernel of
many further tachyon paradoxes (like J.Bell's, F.A.E.Pirani's, J.D.Edmonds' and
others'). The key to the solution is a careful application of tachyon
mechanics, as it unambiguously follows from special relativity. At Last, in one
of the two Appendices, we propose how to evaluate the group-velocity in the
case of evanescent waves. [PACS nos.: 03.30.+p; 03.50.De; 41.20.Jb; 73.40.Gk;
84.40.Az; 42.82.Et ]Comment: LaTeX file: 26 pages, with 5 Figures (and two Appendices). The
original version of this paper appeared in the Journal below
Small Disks and Semiclassical Resonances
We study the effect on quantum spectra of the existence of small circular
disks in a billiard system. In the limit where the disk radii vanish there is
no effect, however this limit is approached very slowly so that even very small
radii have comparatively large effects. We include diffractive orbits which
scatter off the small disks in the periodic orbit expansion. This situation is
formally similar to edge diffraction except that the disk radii introduce a
length scale in the problem such that for wave lengths smaller than the order
of the disk radius we recover the usual semi-classical approximation; however,
for wave lengths larger than the order of the disk radius there is a
qualitatively different behaviour. We test the theory by successfully
estimating the positions of scattering resonances in geometries consisting of
three and four small disks.Comment: Final published version - some changes in the discussion and the
labels on one figure are correcte
Diffractive orbits in isospectral billiards
Isospectral domains are non-isometric regions of space for which the spectra
of the Laplace-Beltrami operator coincide. In the two-dimensional Euclidean
space, instances of such domains have been given. It has been proved for these
examples that the length spectrum, that is the set of the lengths of all
periodic trajectories, coincides as well. However there is no one-to-one
correspondence between the diffractive trajectories. It will be shown here how
the diffractive contributions to the Green functions match nevertheless in a
''one-to-three'' correspondence.Comment: 20 pages, 6 figure
Boundary conditions at spatial infinity for fields in Casimir calculations
The importance of imposing proper boundary conditions for fields at spatial
infinity in the Casimir calculations is elucidated.Comment: 8 pages, 1 figure, submitted to the Proceedings of The Seventh
Workshop QFEXT'05 (Barcelona, September 5-9, 2005
Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. III. On the determination of radiation
We discuss the issue of radiation extraction in asymptotically flat
space-times within the framework of conformal methods for numerical relativity.
Our aim is to show that there exists a well defined and accurate extraction
procedure which mimics the physical measurement process. It operates entirely
intrisically within \scri^+ so that there is no further approximation
necessary apart from the basic assumption that the arena be an asymptotically
flat space-time. We define the notion of a detector at infinity by idealising
local observers in Minkowski space. A detailed discussion is presented for
Maxwell fields and the generalisation to linearised and full gravity is
performed by way of the similar structure of the asymptotic fields.Comment: LaTeX2e,13 pages,2 figure
Resolution of the Klein Paradox
We present a resolution of the Klein paradox within the framework of
one-particle relativistic quantum mechanics. Not only reflection becomes total
but the vacuum remains neutral as well. This is accomplished by replacing the
pair production process with virtual negative energy "incidence" within the
barrier in a similar manner to what is done with image charges in electrostatic
and virtual sources in optics.Comment: 9 pages, 8 figure
Gamma-ray signatures of annihilation to charged leptons in dark matter substructure
Due to their higher concentrations and small internal velocities, Milky Way
subhalos can be at least as important as the smooth halo in accounting for the
GeV positron excess via dark matter annihilation. After showing how this can be
achieved in various scenarios, including in Sommerfeld models, we demonstrate
that, in this case, the diffuse inverse-Compton emission resulting from
electrons and positrons produced in substructure leads to a nearly-isotropic
signal close to the level of the isotropic GeV gamma-ray background seen by
Fermi. Moreover, we show that HESS cosmic-ray electron measurements can be used
to constrain multi-TeV internal bremsstrahlung gamma rays arising from
annihilation to charged leptons.Comment: 8 pages, 4 figures; minor updates to match published versio
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